Smoothing across multiple objects
Yes, this can be done.


keep a single whole object(this is the reference for correct normals).
enable auto-smooth on all broken parts(needed for custom normals to show).
using the Normal Edit modifier on the broken parts to copy the normals from the whole object to the broken parts.


If you want to avoid some slow-downs from continued updates, you can apply the modifiers to store the custom normals.